One rechargeable battery of mass 15.0 g delivers to a CD player an average current of 18.0 mA at

step 1 We know the energy formula that is e is equal to V, I, T, where V is the voltage, I is the curre

One rechargeable battery of mass 15.0 g delivers to a CD...

One rechargeable battery of mass $15.0 \mathrm{g}$ delivers to a CD player an average current of $18.0 \mathrm{mA}$ at $1.60 \mathrm{V}$ for $2.40 \mathrm{h}$ before the battery needs to be recharged. The recharger maintains a potential difference of $2.30 \mathrm{V}$ across the battery and delivers a charging current of $13.5 \mathrm{mA}$ for $4.20 \mathrm{h}$ (a) What is the efficiency of the battery as an energy storage device? (b) How much internal energy is produced in the battery during one charge-discharge cycle? (b) If the battery is surrounded by ideal thermal insulation and has an overall effective specific heat of $975 \mathrm{J} / \mathrm{kg}^{\circ} \mathrm{C},$ by how much will its temperature increase during the cycle?

Key Concepts

Electrical Energy Calculations

Electrical energy calculations are based on the principle that energy can be calculated from the product of voltage, current, and time (E = V × I × t). These calculations are essential for determining both the energy supplied to the battery during charging and the energy delivered to a device during discharge, forming the basis for efficiency and performance evaluations.

Specific Heat and Thermal Energy Conversion

Specific heat is the property of a material that indicates the amount of energy required to raise the temperature of a unit mass of that material by one degree Celsius. In systems like batteries, any energy that is not converted into useful work often appears as an increase in internal energy, leading to a temperature rise, which can be calculated using the specific heat capacity and the mass of the battery.

Battery Energy Efficiency

Battery energy efficiency is a measure of how effectively a battery converts the energy supplied during charging into useful energy delivered during discharge. It is defined as the ratio of the energy output during discharge to the energy input during charging, and it accounts for various losses such as heat generation and conversion inefficiencies.

Charge-Discharge Cycle Energy Analysis

This concept involves evaluating the energy involved in both the charging phase and the discharging phase of a battery. By calculating the total electrical energy delivered (or consumed) over time using the product of current, voltage, and time, one can determine the energy losses that occur during a complete cycle and assess the overall performance of the battery.

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